A major car magazine has recently collected data on 30 leading cars in the U.S.market.It is interested in building a multiple regression model to explain the variation in highway miles.The following correlation matrix has been computed from the data collected:
Based on this information,if we test using a 0.05 level of significance,the critical value for testing whether any of the independent variables are significantly correlated with the dependent variable is t = 2.0484.

Question

A major car magazine has recently collected data on 30 leading cars in the U.S.market.It is interested in building a multiple regression model to explain the variation in highway miles.The following correlation matrix has been computed from the data collected:
  Based on this information,if we test using a 0.05 level of significance,the critical value for testing whether any of the independent variables are significantly correlated with the dependent variable is t = 2.0484.

Quizplus · Accepted Answer

The correlation coefficients between the dependent variable (highway miles) and the independent variables (price, weight, engine size, and horsepower) are all greater than the critical value of 0.371, which means that they are all significantly correlated with highway miles. Therefore, if we test using a 0.05 level of significance, the critical value for testing whether any of the independent variables are significantly correlated with the dependent variable should be larger than 0.371. The given critical value of t = 2.0484 is larger than 0.371, so the statement is true.

A Major Car Magazine Has Recently Collected Data on 30